Problem: If $x \diamond y = x+8y$ and $x \oplus y = 3x-4y$, find $-1 \oplus (-1 \diamond 1)$.
Solution: First, find $-1 \diamond 1$ $ -1 \diamond 1 = -1+(8)(1)$ $ \hphantom{-1 \diamond 1} = 7$ Now, find $-1 \oplus 7$ $ -1 \oplus 7 = (3)(-1)-(4)(7)$ $ \hphantom{-1 \oplus 7} = -31$.